cp's OEIS Frontend

A353138 Sum of (the number of digits in n to the power (each digit in n)).

%I A353138 #55 Apr 27 2023 14:57:52
%S A353138 1,1,1,1,1,1,1,1,1,3,4,6,10,18,34,66,130,258,514,5,6,8,12,20,36,68,
%T A353138 132,260,516,9,10,12,16,24,40,72,136,264,520,17,18,20,24,32,48,80,144,
%U A353138 272,528,33,34,36,40,48,64,96,160,288,544,65,66,68,72,80,96
%N A353138 Sum of (the number of digits in n to the power (each digit in n)).
%C A353138 In base 10, 1 and 4624 are the only numbers where a(n)=n (conjectured).
%C A353138 a(n) < n when n > 2.1*(10^10).
%H A353138 Robert Israel, <a href="/A353138/b353138.txt">Table of n, a(n) for n = 1..10000</a>
%F A353138 a(n) = Sum_{k=1..A055642(n)} (A055642(n))^(floor(n*10^(1-k)) mod 10).
%e A353138 a(3) = 1^3 = 1;
%e A353138 a(164) = 3^1 + 3^6 + 3^4 = 813;
%e A353138 a(4624) = 4^4 + 4^6 + 4^2 + 4^4 = 4624.
%p A353138 f:= proc(n) local m,L,t;
%p A353138   L:= convert(n,base,10);
%p A353138   m:= nops(L);
%p A353138   add(m^t, t=L)
%p A353138 end proc:
%p A353138 map(f, [$1..100]);
%o A353138 (Python)
%o A353138 def a(n): s = str(n); return sum(len(s)**int(d) for d in s)
%o A353138 print([a(n) for n in range(1, 101)]) # _Michael S. Branicky_, Apr 26 2022
%o A353138 (PARI) a(n) = my(d=digits(n)); vecsum(vector(#d, k, #d^d[k])); \\ _Michel Marcus_, Apr 27 2022
%Y A353138 Cf. A055642, A101337.
%K A353138 nonn,look,base
%O A353138 1,10
%A A353138 _William Halpin_, Apr 26 2022